Preheat the oven to 325 degrees F (165 degrees C). Grease a 9x13-inch baking dish.

Combine brownie mix, eggs, water, and oil in a large bowl; stir until well blended. Spread mixture evenly into the prepared dish.

Bake in the preheated oven until top is dry and edges have started to pull away from the sides of the pan, 20 to 25 minutes. Cool completely, about 30 minutes. Cut brownie into 1-inch squares.

Beat cream cheese in a large bowl with an electric mixer until smooth. Add milk and pudding mix; beat until smooth. Fold in whipped topping until well incorporated into filling.

Place 1/2 of the brownie squares into the bottom of a trifle bowl or glass serving dish; top with 1/2 of the filling. Shave 1/2 of the chocolate almond bark over filling using a vegetable peeler. Top with remaining brownies, filling, and chocolate bark shavings. Refrigerate trifle until set, about 1 hour.